That can get long and tiring if you aren't flying!
There are direct flights and trains for this journey. Travelling by train is the cheapest way of getting there. Mumbai (Maharashtra) to New Delhi (Delhi) distance is 1428 km and you can get there by train in just over 28 hours and 30 minutes. However, flight tickets come also cheap with fares starting from ₹ 4098.
It's gonna be warm and sunny, and did I mention warm ?